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max of k consecutive integers, coprime with divisors of 8775

Source: 2017 Ecuador Juniors (OMEC) L2 p5

October 24, 2022

number theoryconsecutivecoprimeDivisors

Problem Statement

Two positive integers are coprime if their greatest common divisor is

1

. Let

C

be the set of all divisors of the number

8775

that are greater than

1

. A set of

k

consecutive positive integers satisfies that each of them is coprime with some element of

C

. Determine the largest possible value of

K